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She later told the House of Commons that the deal held out the prospect of a zero-tariff free trade area with the EU of a kind the bloc had never previously offered.

And she said: "The British people want Brexit to be settled, they want a good deal that sets us on a course for a brighter future, and they want us to come together as a country and to move on to focus on the big issues at home, like our NHS.

"The deal that will enable us to do this is now within our grasp. In these crucial 72 hours ahead, I will do everything possible to deliver it for the British people."

As she addressed MPs, it emerged that a late change to the UK's draft withdrawal agreement would allow the 21-month transition period after Brexit day to be extended beyond the expected date of the next general election in June 2022.

Where the agreement had offered the possibility of a one-off extension from December 31 2020 to "December 20XX", it now reads "for up to one or two years".

This could mean the transitional period - during which the UK must follow Brussels regulations while having no say over them - could stretch until the end of December 2022, six months after the election date and six and a half years after the 2016 referendum.

The draft political declaration was agreed in principle on Thursday morning, after negotiators worked through the night on new directions issued by Mrs May and European Commission president Jean-Claude Juncker when they met in the Belgian capital on Wednesday evening.

The breakthrough cleared the way for a special summit in Brussels on Sunday, at which leaders of the remaining 27 EU states are expected to give their stamp of approval to both the future framework and a separate withdrawal agreement setting out the terms of the UK's departure.

Mrs May briefed members of her Cabinet on the new text in a conference call and was addressing MPs in a statement to the House of Commons later in the day.

Speaking outside Number 10, she said: "This is the right deal for the UK. It delivers on the vote of the referendum, it brings back control of our borders, our money and our laws and it does so while protecting jobs, protecting our security and protecting the integrity of the United Kingdom."

Confirming that she would return to Brussels on Saturday for further talks with Mr Juncker ahead of the summit, she added: "The British people want this to be settled, they want a good deal that sets us on course for a brighter future.

"That deal is within our grasp and I am determined to deliver on it."

Agreement on the text was announced by European Council president Donald Tusk, who said in a tweet: "I have just sent to EU27 a draft Political Declaration on the Future Relationship between EU and UK.

"The Commission President has informed me that it has been agreed at negotiators' level and agreed in principle at political level, subject to the endorsement of the leaders."

Downing Street has always stressed that the 585-page legally binding withdrawal agreement setting out the terms of the UK's departure from the EU - including a "divorce bill" estimated at £39 billion - can only be finalised alongside the shorter declaration setting out the two sides' aspirations for their future relations.

Mrs May will hope that the prospect of an ambitious free trade deal set out in the 26-page declaration will win over some of the Conservative MPs who have voiced deep misgivings about her plans.

The new text calls for an "ambitious, broad, deep and flexible partnership" covering trade, law enforcement, foreign policy, security and defence, which could take the form of a Ukraine-style Association Agreement.

It confirms that the future relationship must respect the sovereignty of the UK and its right to develop an independent trade policy and end the free movement of EU nationals.

And it leaves open the possibility of using technological solutions to keep the Irish border open after Brexit.

But other elements of the declaration angered Brexiteers, including:

• Plans for a "free trade area, combining deep regulatory and customs co-operation", building and improving on the "single customs territory" provided for in the withdrawal agreement;

• A commitment to "work together" on safeguarding workers' rights and consumer and environmental protections;

• Provisions to ensure a "level playing field" on business competition, which could cover areas including state aid, climate change laws and tax;

• A role for the European Court of Justice in providing "binding" rulings on the interpretation of EU law in any disputes between the two sides.

The document envisages negotiations beginning immediately after the formal date of Brexit on March 29 2019, with high-level conferences every six months. Agreements on "equivalence" of financial services regulations and access and quotas for fishing should be reached in time to come into effect at the end of the transition period on December 31 2020.

The new text was dismissed by First Minister Nicola Sturgeon as "lots of unicorns taking the place of facts about the future relationship".

Leave-backing Tory MP Marcus Fysh said that the political declaration made Mrs May's withdrawal agreement "even more toxic".

And a source from the European Research Group of eurosceptic Conservative MPs said: "The political declaration is not legally binding, vague, aspirational and little more than a smokescreen to cover up the fact that the permanent relationship is the customs union backstop."

Conservative MP Philip Lee, who quit the Government in protest at its handling of Brexit, said it "reads like a letter to Santa", while Labour's Chuka Umunna, a leading supporter of the People's Vote campaign for a second referendum, said it was "entirely aspirational and doesn't finalise anything".

"This is a terrible offer to the British people and one that the people should have the opportunity to turn down in favour of keeping our current deal as members with a say over decisions that affect our future," said Mr Umunna.